by Omar Ali

Trump has been elected President. Having participated in a week-long social media freakout to deal with this shock (a fact I did not recognize about myself until a couple of days ago), I have some thoughts and I would like to put them out so that I can be enlightened by feedback. It is the only way to learn.

Very qualified people have written some good pieces already about the why and the how. I am posting links to them below, along with some random thoughts about the articles. They are not the whole story (what is?) but I think all these articles are must reads. My own comments are more like invitations to tell me off, or tell me more…

After these links and comments, I sum up my own thoughts and end with some questions.

You are still crying wolf, from Slate Star Codex. (I don't think Trump is particularly racist or sexist (relative to most 70 year old males, of any ethnicity) and he is obviously socially liberal compared to traditional Republicans. But the possibility is there that this shallow man (more or less socially liberal, a conman, ignorant) will be manipulated by his newfound advisers into disasters (initially abroad) that could have endless branching and mutating unintended consequences here and abroad. That could be a truly transformative crisis… Racism and the rise of the KKK (real and imagined) are small potatoes compared to the storms that could potentially be unleashed in the world… Muslims, being intimately connected to the worldwide crisis in very direct ways, will likely face the consequences within the USA too; but the crucial point is that the whole shitstorm is likely to proceed along tracks that are occasionally parallel, but mostly completely unconnected with the identitarian postmarxist postmodern worldview that dominates the elite Eurocentric Left today… Incidentally, if the ordure does hit the fan (I hope it does not, i hope the much-maligned current world order survives or at least, has a soft landing), then Blacks and Latinos, like other citizens, will fight for America. I suspect that the fantasy worldview that emphasizes supranational and subnational identities well above national ones will prove very flimsy; flimsier even than “class solidarity” proved to be in the first world war…the elite Left's freakout about the KKK and the coming age of Jim Crow is not completely wrong, but misses the biggest threats and their likely consequences. Which is not to say that no connection can be made between racism and the international order, but the race-obsessed post-truth glasses of the new postmarxist Left do get them into endless wrong turns and dead-ends in terms of priorities to be tackled.

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by Humera Afridi

Gündüz Vassaf's latest book, What Can I Do, arrived like manna this past summer, a panacea for our times, urging action as an antidote to pessimism. The book's publication in Turkey coincided with the heightened and volatile political climate in the country in the immediate aftermath of the failed coup attempt. Its message couldn't be more pertinent. Certainly, post-election America, traumatized and rattled by aftershocks, could do with just such a guide. The need for an English translation of What Can I Do? feels ever more critical.

On November 4, 2016, days before the US elections, writing from Ortigia, Sicily, Vassaf dispatched a prescient letter to editors of several international newspapers, stating with clarity what's exactly at stake in the US elections: “It's not just who the candidates are. America is too important for the world. And the world is too important to be left to America.” Here we find ourselves now, inhabiting an altered reality post-election, and Vassaf's disavowal of pessimism in favor of action resonates powerfully, offering a means of harnessing our ability to create the change we want to see.

The idea of freedom is a leitmotif in Gündüz Vassaf's work. Freedom is something he is conscious of in all aspects of life, both visible and unseen. It's a subject he delves into in an earlier book, Prisoners of Ourselves. Freedom is, too, a practice he embodies daily, certainly through his creativity, upholding the ideal of a life liberated from artificial and internalized constraints. The day we met, I noticed with surprised delight that he prefers to walk barefoot around the island where he resides in the summer, utterly at ease traversing the stony ground without shoes. Moments after introductions were exchanged, Vassaf suggested a swim, and a small group of us waded into the blue-green Sea of Marmara, as if we'd been friends forever. I marveled at my own readiness to discard formality in Vassaf's company, noting his talent for opening the way to an honest, satisfying experience of reality, stripped of convention and inhibition.

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by Ali Minai

It is the worst of times. Period! The presidential election of 2016 possibly represents a hinge-point in American like no other since the beginning of the Cold War, though perhaps an argument can be made for 9-11. Indeed, September 11, 2001 and November 8, 2016 may be seen as two ends of the same massive hinge that has turned that entire course of American — and, therefore, world — history in a different direction.

Within the domestic context of the United States, it is hard to see the election of Donald Trump to the American presidency as anything other than the ignition of a new civil conflict along ideological lines. It is not a “civil war”, but the weapons involved will be no less destructive to the fabric of society.

The arrival of this conflict is not a surprise since there have been hints of it for years, but its current modality is a huge shock. Tensions have been building up in the United States for decades as it turns inexorably towards becoming a multi-racial, multi-ethnic, multi-religious society. Power has been siphoning away from the mainly white elite defined by tradition and becoming distributed over a more diverse elite defined by education and technical competence. The largest group “left behind” in this process is the non-elite largely white population that, long conditioned to accept the supremacy of the traditional elite, suddenly finds itself facing competition from unskilled Latin American labor and the ascendancy of a new diverse and global elite. Saying “I want my country back” is a natural response in this situation. It is impossible for this sentiment not to have an ethnic subtext — though it is an oversimplification to see the conflict as primarily racial, ethnic or religious. These factors are important signifiers, but the core issue is a fundamental difference in worldviews.

Add in the devastation of rural America by poverty and drugs, the stoking of religious tensions by 9-11, endless wars fought by soldiers from the lower economic strata, the disdainful attitude of the new liberal elites, and one has a toxic brew of resentment bubbling in the white working class (WWC) throughout the country. The only question was whether this boiling hot mess would subside as the cold water of demographic reality drizzled on it, or if it would come to a boil. Obama’s election in 2008 and 2012 seemed to suggest that it might be cooling down. Unfortunately, not so!

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by Paul North

The Anti-Christ—we know who he is.

Thessalonians says: “And then the lawless one will be revealed” (2:8).

The end arrives for human beings in the worst imaginable form, a demi-god who tears down the world they have carefully built. Wickedness and destruction overtake goodness and progress. Certainly he doesn't do this openly. He insinuates himself through spectacular deceptions. “He will use all sorts of displays of power through signs and wonders that serve the lie” (2:9). This is the moment that 2 John calls “the last hour,” because this fate, the destruction of everything, is also supposed to be the gateway to a new first hour, to final redemption. The coming of the Anti-Christ is the worst fate imaginable, but it also means that now things can only get better. “And then the lawless one will be revealed, whom the Lord Jesus will overthrow with the breath of his mouth and destroy by the splendor of his coming” (2:8).

Before redemption comes of course, everything truly has to be crushed to smithereens. This bargain—total destruction for total restitution—belongs to the modern fate idea as well. The popular sayings: “things can only get better,” “every cloud has a silver lining,” and most directly “it is always darkest before the dawn” express and reinforce the idea that this is an inevitable trade off. We accept destruction because it leads to restoration. Thinking like this of course, some may be tempted to help hasten the decline. Martin Luther famously advised his colleague Melanchthon in 1521 to “be a sinner and let your sins be strong.” There is an insidious logic here. Without strong sins leading up to it, redemption can only be weak. The very idea of redemption—a strong correction in the course of the world—requires that the world be on a very bad course indeed. If the world just drifts, or remains at a low stage of decrepitude, it is hard to imagine it can be saved. One could thus turn this around and say that redemption thinking often leads to the acceptance of destruction as a necessary evil.

In any case, fateful thinking is a tranquilizer after catastrophic events. These sorts of thoughts bubble up: “it had to happen this way,” “the world is really like this,” or even “if we hadn't ignored the signs, this would not have happened.” But it did happen, our fatal flaw let fate take its course. In the wake of the terrible event, we write it back into the story of how things inevitably were going to go.

And when he is finally here, when the Anti-Christ arrives, the run of the mill believer is helpless. The great battle will be fought between Christ and Anti-Christ, opposed cosmic forces. We may not intervene. So we repeat those stock phrases, every cloud has…, it's always darkest…, and so on. The battle has been forecast from time immemorial and we are only along for the ride.

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by Dave Maier

On the afternoon of Election Day, I was in the local library doing a particularly nasty jigsaw puzzle (I like to do them at the library, because they have such big tables there that you can spread out as much as you want), and I happened to overhear a conversation among a man and two women, all strangers. All three were thirty-somethings with children (as became clear). The guy had been working at his laptop when the women, whom he knew, came in, and soon he was regaling them with a story of his morning spent dealing with this and that. He told it well, and was very engaging and likable, and his audience responded appropriately. They did not strike me as in any way deplorable (except possibly that they were talking loudly in the library).

I say this because, even before one of the women (later on in the conversation) said something like “I like the way he tells it like it is!”, I found myself with no doubt whatsoever that these were Trump supporters. In the aftermath of that disaster (by which I was not nearly as surprised as some, possibly because of this incident in the library), I have been wondering what to think about those on the winning side. I haven’t come to any conclusions, and clearly there are a number of different reasons one might have voted red this year; but if anyone needs more disjointed post-election ramblings, you’ve come to the right place. No doubt they say more about me than about the world; in any case, that’s all I’ll be good for for a while. Best of luck to anyone else trying to figure it out for themselves as well.

Why did I believe, or how did I know, that the by-librarians-unaccountably-unshushed trio were Trumpians, even before it was confirmed? They had not been discussing politics or culture or anything close to it; the guy’s mother couldn’t start her car, and the globalist elite was not apparently at fault. I think it was just their manner: they seemed somehow to revel in their just-ordinary-folks unpretentiousness, even though socio-economically they were clearly upwardly mobile middle-class citizens of our fairly upscale community rather than the economically stressed white working class we keep hearing about. I found myself with an uncanny impression that if they knew me they would regard me as perversely elitist, quite independently of my views themselves. Indeed I do regard the main appeal of Trumpism to otherwise non-deplorable people as a celebration of (what they perceive as) “ordinary” life and a salutary rejection of what in contrast is perversely unordinary. The latter need not be the obvious things; in fact I feel sure that if I were merely black or gay or Muslim or Latino, rather than white and straight and weird, they would be perfectly okay with me. But who knows?

For some perspective on this, let’s look at some other data points that have been bouncing around my head in the last week.

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by Michael Liss

We got our butts kicked, and kicked very hard. Adlai Stevenson, ruminating about the results of the 1952 Election, recalled Abraham Lincoln's reaction to an electoral loss: We are like the boy who stubbed his toe—it hurts too much to laugh, and we are too old to cry.

It's a few days later, and the damaged digit still aches, so let's take off the shoe and get a closer look. Nasty—swollen with punctured pride and inflated expectation. And, is that yellowish stuff pus?

There is no delicate way to describe why and how this wrenching event occurred. Nor is there any comfort in speculating just what our new leaders in Washington have planned for us. But we need to. If we don't dive in, take our medicine, and prepare for the future history will repeat itself.

We can begin the post mortem with the Clinton campaign's primary complaints: unfair coverage by the mainstream media, and James Comey's intercession. To that, I am going to add the dedicated Trump team at WikiLeaks.

Ah, the press, you can't live with them, you can't live without them. They loved Trump—even though he threatened and mistreated them, he was great copy, he made news constantly, which drew eyeballs and advertiser dollars. To balance out their reporting of Trump's excesses (all Trump had was excesses) they felt compelled to add an equal dollop of negative Hillary stories. To the Clinton's campaign's collective way of thinking, this constantly created a false equivalence of two sinners. Fair? Kind of. I give it 5 out of a possible 10 on the biased scale.

Comey? Very difficult to evaluate. I don't want to impugn his motives and I think he was genuinely conflicted. What we don't know is how many votes he moved because we don't have hard, reliable data. Even with that qualifier, we can't discount the impact of Comey's choices and the possibility that his decisions changed both the Presidential and down-ballot races. I think he is an honorable man—and, because he's an honorable man, he probably is losing sleep over this—and should. 8 out of 10, with the potential for an upward revision.

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by Leanne Ogasawara

Turin is a city which entices a writer towards vigor, linearity, style. It encourages logic, and through logic it opens the way towards madness. —Italo Calvino

Just a short walk down the portico-covered arcades of Via Roma leads to one of the most elegant Baroque squares in Turin– if not, in all the world…

We were in town to see a particular picture; for Turin is home to a precious painting of Saint Francis receiving the stigmata. Attributed to van Eyck, the picture has an exact –but much larger size– copy in Philadelphia; and art historians have gone back and forth over the years about which one is the copy of which. Both paintings were believed to have been part of the 1471 inventory of the will of none other than Anselm Adornes, the fabulously wealthy Bruges merchant (who happens to be a great obsession of mine).

It seems strange to have two identical paintings created, when the cost was so high to buy a van Eyck, but it turns out that back in the 15th century, the super wealthy sometimes had different sizes of a painting created so they would be able to bring the smaller version with them when they traveled or perhaps give one to a daughter on her wedding day. Why not, right? It is possible the smaller version of the van Eyck, held in the Sabauda Gallery in Turin, was created for just this purpose.

The painting does not disappoint and it was well worth the trip–but to say we got distracted along the way would only be an understatement.

For me, it started sitting in a cafe in the Piazza San Carlo. The piazza is, as I suggested above, possibly the most beautiful square in the world. Being the capital of the House of Savoy, the city is in many ways more French-feeling than Italian. With its standardized building facades made of huge pieces of cut stone adorned with tall windows and wrought iron balconies, the city evokes a more Northern, noble atmosphere. Like Paris, it is a city built for kings. But rather than in the grand boulevards one finds in Paris, in Turin, it is the piazza where the Baroque architecture dazzles.

And no where dazzles more than the Piazza San Carlo.

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by Evan Edwards

Sometime in November 1944, the U.K. based Vegetarian Society splintered slightly when several members—calling themselves “Vegans”—came to believe that simply abstaining from eating animal flesh did not go far enough in alleviating the suffering of animals. Vegans, if you don’t already know, argue that if one of the pillars of the vegetarian ethos is to not contribute to the death and suffering of animals, then to continue to take milk from nursing cows, wear leather stripped from their bodies, to subject hens to miserable living conditions for eggs, and so on, is in fact not to live up to stated ideals.

Never before in the long and complex history of vegetarianism had such a distinction been made. For thousands of years, philosophers and religious figures had made ethical and health-based arguments for not making one’s body “a tomb”—as Leonardo da Vinci reportedly put it—but the exact meaning and limits of this abstention were never quite defined. Some, thinking that fish were not really ‘animals’—in many romance languages, seafood translates most literally as “fruits of the sea”—allowed for their consumption, others like Pythagoras included legumes in the list of forbidden fare for reasons unknown. But due to reason or circumstance, the Vegan Society believed that this ambiguity about what constitutes suffering and cruelty was ripe for clarification.

Perhaps, on a grand historical level, the shift from subsistence farming to mass industrial schemes that accompanied the modern era had brought the evil of these forms of animal exploitation into focus. Perhaps it was due to a heightened awareness of the unfathomable depths to which suffering could sink, brought about by these individuals’ own subjection to a war that had been raging for nearly five years in their home country, a war that had brought the London Blitz, the bombing of Dresden, a total war that summoned as from hell itself the factory-like conditions of the Nazi work-camps, which had delivered more carnage than any war in history, and which had yet to show its greatest instrument of cruelty, the atomic bomb. Perhaps it was just coincidence or fate, because in 1994, to commemorate the break, the Vegan Society declared November “World Vegan Month,” ironically during the very time when over 50 million Turkeys are getting their last plump-up before their national slaughter in America.

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by Matt McKenna

A population of complacent optimists unexpectedly find themselves at the mercy of a ghastly ogre: Is this the story of the Democrats in 2016 or the plot of DreamWorks’ new animated film, Trolls? As liberal American adults come to grips with how their country could elect the relatively progressive Barack Obama to the Presidency twice in a row only to immediately elect the much less progressive Donald Trump, children around the world are watching Trolls, a hard hitting metaphor for the 2016 U.S. Presidential election.

The filmmakers deserve credit for coming up with a ninety-minute movie based on nothing more than the license for a brand of goofy dolls that was last culturally relevant back in the 1990s along with other collectibles such as Beanie Babies, Furbies, and Pokemon. To turn the toy line into a movie franchise, the screenwriters gifted the Trolls with a strange backstory: Within their songful, permanently optimistic society, the Trolls’ only problem is that they are hunted by the Bergen, a diseased-looking band of ogres who find happiness only in eating the little Trolls. Every year, in fact, the Bergen enjoy a festival called “Trollstice” in which the normally mopey, grumpy, and unpleasant Bergen feast upon the bodies of the radiant Trolls to attain momentary contentment. Unsurprisingly, the Trolls eventually tire of being eaten, and they escape Bergentown by hiding in a nearby forest. After a brief chase, all the Bergen–save one–give up looking for them, and the Trolls appear to be safe forever.

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by Bill Benzon

Dan Everett. Dark Matter of the Mind: The Culturally Articulated Unconscious. University of Chicago Press, 2016.

I want to approach Everett’s dark matter indirectly. In 1973 David Hays, who soon became my teacher, published an article entitled, “Language and Interpersonal Relationships” [1]. It begins with a simple one-sentence paragraph: “How does language engender love?”

That’s certainly not a question that’s central to linguistics or even peripheral to it. But it was central to Hays’s understanding of language and, if I read him rightly, it’s a question Everett would understand. For both of them see language in the context of social interaction. How natural, you might say, for language is a means of communication, no? Yes, it is. But much of the most important and influential thinking about language over the past six decades, thinking catalyzed by the work of Noam Chomsky, sees language primarily as a tool of thought and only secondarily as a tool of communication. How peculiar, you say, how very peculiar.

Exactly.

Hays went on to discuss communication, reporting that Harold Garfinkel once had his undergraduate students “write down what the participants in a conversation actually said, then in parallel what they understood the participants to be talking about.” Garfinkel concluded that much was unsaid. Much of what’s unsaid belongs to the mind’s dark matter. Some of it could be said if the conversation required it, but much of it could not.

Consider a wellknown thought experiment, something of a parable if you will, by Herbert Simon [2]. He asks us to imagine an ant walking on the beach. Its path is complex, irregular, and difficult to describe. Does that mean the ant had complex intentions and capabilities? No, the ant’s intentions and capabilities were simple, but it pursued them in a complex world, a beach littered with debris and marked with the cliffs and valleys traced the weather, the water, and by larger creatures. In that world the pursuit of a simple purpose by simple means led the ant to trace a complex path.

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by Scott F. Aikin and Robert B. Talisse

When we tell people that we write about logic and politics, we let our interlocutors make the big joke. There is no logic in politics! It's a funny joke, for sure. But it's also tragic. And the tragedy is double-barreled. First, good reasons should be behind decision making. Without good reasoning, policy will likely be an irrational hash. There may be no logic in politics, but there ought to be. Second, the politics referred to in the quip is the politics of our democracy. And in a democracy what's true of the politics is often true of the participants. This includes not only the candidates, politicians, lobbyists, and media personalities, but the citizens as well. And it's hard to deny that we, the democratic citizens, are not users of logic when it comes to politics. The joke's on us.

As the current election cycle grinds to its finish, we easily see the toll it has taken on us. As a democratic nation, we are fatigued. We are so exhausted by our politics that it has become a common theme on the news channels and the late night comedy shows. Keeping up with the latest scandal, press release, spin, poll, and decision from governmental investigative institutions has worn us down. Moreover, the months of daily demands for outrage, disgust, and indignation have left the nation drained. Were such a thing conceptually possible, a clever politician would mandate a moratorium on politics beginning on November 9.

There is good news and bad news about our weariness. The bad news is that many of the items that have consumed the citizenry's attention of late have sapped us in a way that has diluted our trust in democracy itself. It is a common observation among democracy's enthusiasts that democracy is, even at its best, hard to love. But it really shouldn't be this easy to despise. The country has spent months feeding on a forced diet of doomsday politics, with each candidate and nearly every political officeholder given an abundance of reasons for thinking that November 8, 2016 marks the beginning of the End Times for democracy. When this message is accompanied by an “unless” clause that conveniently identifies the speaker, his Party, of his favored candidate as the country's only savior, the nausea is only exacerbated. The full-tilt political season, now arguably in its fourteenth consecutive month, has been not only something difficult to endure. It has provided good reason to wonder whether self-government is worth all the psychological trauma.

The good news comes on a few fronts, but is in no case untarnished. The first is that things are almost over. The country votes tomorrow. That brings an end to the phone calls and the advertisements and all of the unbelievably hostile discussions on television news channels.

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by Shadab Zeest Hashmi

One point six miles from the Pacific, the house with the terra cotta fountain and the carob tree, on Crescent Point Road.

You all came home in rear-facing car seats, swaddled in blankets and matching caps, different colors, different years, but from the same hospital, about ten miles away from here. Each of you was less than a week old at circumcision; Babay looked away at that unbearable moment when you were clamped down for the operation while I learned to cradle your head with one hand and dip your pacifier in sugar water with the other; if you rejected the pacifier, I dipped my finger in sugar water and let you suck on it—all the while speaking to you and praying the Qul in your ear. In those few minutes of excruciating pain for us all, I discovered the emboldening surge of what they call the maternal instinct; I discovered my power to protect and soothe, my voice and touch suddenly transformed by some visceral spell—an empowerment like no other.

Since then, I’ve learned that “rahm” or “womb” is the root of “ArRahmaan,” the most exalted of the ninety-nine names of God; Divine compassion is exemplified in the mother’s instinct to protect and nurture. All the years I’ve been raising you, I’ve trusted this love to guide me. I’ve taught you Islamic values, I’ve taught you American values. I’ve taught you that, contrary to the dominant picture, these values are aligned with each other: respect for divergent beliefs, a strong work ethic, a sense of egalitarianism and justice, cultivating independent thought while engaging in meaningful dialogue, stewardship of the planet, are part of both the Islamic and the American ethos. The world you have grown up in has been savage in acute ways, ways that history will eventually dissect and explain, but you, young Muslims, may arguably be the primary target of the war-terrorism binary which has resulted in a chilling polarization. Against this rising and brutal divide, I’ve taught you that your Muslim-American identity is inherently harmonious and that you must develop an immunity to the poisons of ignorance, politically motivated prejudice and manufactured fear of the other. And that there is no better anti-poison than reading; read widely, read deeply— remember the first Quranic word: “Iqra!” or “Read!”

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by Patrick Lee Miller

Trump is contemptuous of truth. It is not so much that he lies, although obviously he does a lot of that. His contempt of truth goes deeper than that of the liar, who knows what’s true and deliberately says the opposite. Trump simply doesn’t care whether what he says is true or false. A Princeton philosopher, Harry Frankfurt, called this attitude bullshit in an essay he wrote under that title decades ago. A canny publisher recognized an audience for the distinction between lying and bullshitting during the junior Bush years and put out the same essay as a little book.[1] Frankfurt had his fifteen minutes of fame on Jon Stewart’s show and then faded from public awareness. His distinction lives on, but it was never really his in the first place. Plato first drew it to alert his countrymen to the dangers of the Sophists.

These were famous men who traveled the Greek world selling their power with words. Words are always potent tools, but more so in democratic societies such as classical Athens, where political office can be acquired by making speeches. When you can manipulate words, you can sway crowds. The Sophists became rich, and in a few cases powerful, by promising to make their customers masters of words. As Plato shows, their expertise was an ability to bullshit, in Frankfurt’s sense. The Sophist knows how to say what it takes to win—a court case, a business deal, a democratic election. He doesn’t care whether what he says is true or false; it’s irrelevant. After a while, in fact, he stops paying any attention to the truth. Thinking about it becomes a distraction from his purpose. Life is a contest, whether for money, fame, or power—and words are the tools for winning.

Plato’s analysis of bullshit goes deeper than Frankfurt’s because it marries a discussion of truth with an understanding of tyranny that helps us understand, among other things, the candidacy of Trump for president.

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by Jonathan Kujawa

On November 8th everyone will be counting. Counting can be hard. Especially in messy real world situations like elections. But in pure mathematics we get to decide the questions in which we are interested. We can choose to count countable things. The secret to math is the art of asking “good” questions. A good question is one in which you can make progress and learn something you didn't know before.

Like Goldilocks, a mathematician looks for questions which are neither too easy nor too hard. An easy problem is boring, unenlightening, and not much fun — a 2x2x2 Rubik's cube of mathematics. But, like a 7x7x7 cube, a too difficult problem is also boring, unenlightening, and not much fun. The secret is to land somewhere in the middle.

If we want to count, we should start by picking something easy to count, but with the promise of mystery. When I was in elementary school we spent hours and hours playing Dots and Boxes. This is the game in which you draw a grid of dots on a sheet of paper. The players take turns drawing horizontal and vertical line segments between dots trying to enclose boxes while blocking your friend from doing the same. The person with the most boxes at the end, wins. You can play it against a computer here.

If I had played less Dots and Boxes and paid more attention in my math classes, I would have learned that our initial dots were nothing but lattice points. These are the points in the xy-plane where both coordinates are an integer. So (1,3), (0,-6), and (2,127) are lattice points, but (1, 3/2) and (1.6, π) are not. Lattice points are easy to count in any geometric shape we may draw. For example, here is a 3×3 square with lattice points for corners:

Counting we see there are 12 lattice points on the sides of the square and 4 in the interior. Stuck in a boring math class for long enough, we might even notice that the area of the square, 9, is also what we get from 12/2 + 4 – 1. And that a 1×1 square has area 4/2 + 0 – 1 and that 2×2 square has area 8/2 + 1 – 1. In fact, it seems like for any square we draw if it has S lattice points on the sides and M lattice points on the interior, then the area always works out to exactly equal S/2 + M – 1. A strange coincidence, indeed! This is when our mathematical sense starts tingling. Coincidences are rare in math.

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